Relative Standard Deviation
When to use relative standard deviation
It is advised to use this formula in the following situations, which are some of the most typical ones:
What is relative standard deviation?
When comparing a set of data’s standard deviation to the mean, relative standard deviation—also known as RSD or the coefficient of variation—is used to assess whether it is small or large. In other words, you can determine the accuracy of your results’ average by looking at the relative standard deviation. However, it can also be applied in the business world when analyzing finances and the stock market. This formula is most frequently used in chemistry, statistics, and other math-related settings.
A set of data’s relative standard deviation can be represented numerically or as a percentage. The results are more skewed away from the data’s mean the higher the relative standard deviation. Conversely, a lower relative standard deviation denotes a more accurate measurement of the data.
How to calculate relative standard deviation
The relative standard deviation is calculated using the formula below:
(S x 100)/x = relative standard deviation
S denotes the standard deviation, and x denotes the mean of the data being used in this formula. The steps to use this formula to calculate the relative standard deviation are as follows:
Examples of using relative standard deviation
Examples of how to determine the relative standard deviation using various scenarios are as follows:
Example 1
You want to find a set of numbers’ relative standard deviation. The values of the set of numbers are 50, 47, 54, and 62. You’ve already determined that this set of numbers’ standard deviation is 2 5. Find the mean of the set before calculating the relative standard deviation. The four numbers can be added up and divided by four (the number of values in the set) to determine the mean. So, 50 + 47 + 54 + 62 equals 213. You will then divide 213 by 4 to get 53. 25. This means that the mean of the sample is 53. 25.
Using the following formula, (S x 100)/x = relative standard deviation, you will have all the data necessary to calculate the relative standard deviation once you have determined the mean. In this formula, S is equal to 2. 5 and x is equal to 53. 25. So, 2. 5 multiple by 100 equals 250.
You will then divide 250 by 53. 25 to get 4. 69. This indicates that the set of numbers’ relative standard deviation is equal to 4 69. This indicates that most of the numbers in your sample would fall within a range of +/- 4. Most, if not all, of the numbers will fall between 48 and 69 of your mean. 56 and 57. 94.
Example 2
In order to calculate the relative standard deviation of a set of data relating to its stock value over the previous five years, Company XYZ wants to. The sample used has the following numbers: 25, 23, 27, 29, 32, and 26. The standard deviation for this sample is 5. Finding the sample mean is the first step in calculating the relative standard deviation. Consequently, 25 + 23 + 27 + 29 + 32 + 26 = 162 The result is 27 when this number is divided by the sample size of six. As a result, 27 is the mean, or average, of the given set of numbers.
*Once the mean has been established, the business must use the formula to determine the relative standard deviation. (S x 100)/x = relative standard deviation is the formula. *.
S (the standard deviation) in this problem is equal to 5, and x (the mean) is equal to 27. So, 5 multiplied by 100 equals 500. 500 divided by 27 equals 18. 5. This indicates that the sample’s relative standard deviation is 18 5.
FAQ
How do we calculate the relative standard deviation?
- (S x 100)/x = relative standard deviation.
- You want to find a set of numbers’ relative standard deviation.
- You will then divide 250 by 53.25 to get 4.69.
How do you calculate relative standard deviation in Excel?
Relative Standard Deviation in Excel To obtain the mean and standard deviation, combine the following commands, then multiply the result by 100: =average(a1:A10) =std dev(a1:A10)
How do you find relative standard deviation by hand?
The coefficient of variation’s absolute value is known as the relative standard deviation (RSD or%RSD). It is often expressed as a percentage.
What is RSD in statistics?
The coefficient of variation’s absolute value is known as the relative standard deviation (RSD or%RSD). It is often expressed as a percentage.
